IDEAS home Printed from https://ideas.repec.org/p/fip/fedgfe/2015-50.html
   My bibliography  Save this paper

High-Dimensional Copula-Based Distributions with Mixed Frequency Data

Author

Abstract

This paper proposes a new model for high-dimensional distributions of asset returns that utilizes mixed frequency data and copulas. The dependence between returns is decomposed into linear and nonlinear components, enabling the use of high frequency data to accurately forecast linear dependence, and a new class of copulas designed to capture nonlinear dependence among the resulting uncorrelated, low frequency, residuals. Estimation of the new class of copulas is conducted using composite likelihood, facilitating applications involving hundreds of variables. In- and out-of-sample tests confirm the superiority of the proposed models applied to daily returns on constituents of the S&P 100 index.

Suggested Citation

  • Dong Hwan Oh & Andrew J. Patton, 2015. "High-Dimensional Copula-Based Distributions with Mixed Frequency Data," Finance and Economics Discussion Series 2015-50, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgfe:2015-50
    DOI: 10.17016/FEDS.2015.050
    as

    Download full text from publisher

    File URL: http://www.federalreserve.gov/econresdata/feds/2015/files/2015050pap.pdf
    File Function: Full text
    Download Restriction: no

    File URL: http://dx.doi.org/10.17016/FEDS.2015.050
    File Function: http://dx.doi.org/10.17016/FEDS.2015.050
    Download Restriction: no

    File URL: https://libkey.io/10.17016/FEDS.2015.050?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Lee, Tae-Hwy & Long, Xiangdong, 2009. "Copula-based multivariate GARCH model with uncorrelated dependent errors," Journal of Econometrics, Elsevier, vol. 150(2), pages 207-218, June.
    2. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    3. Maheu, John M. & McCurdy, Thomas H., 2011. "Do high-frequency measures of volatility improve forecasts of return distributions?," Journal of Econometrics, Elsevier, vol. 160(1), pages 69-76, January.
    4. Dong Hwan Oh & Andrew J. Patton, 2018. "Time-Varying Systemic Risk: Evidence From a Dynamic Copula Model of CDS Spreads," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 181-195, April.
    5. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464.
    6. Nikolaus Hautsch & Lada M. Kyj & Peter Malec, 2015. "Do High‐Frequency Data Improve High‐Dimensional Portfolio Allocations?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(2), pages 263-290, March.
    7. Xin Jin & John M. Maheu, 2013. "Modeling Realized Covariances and Returns," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 11(2), pages 335-369, March.
    8. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(2), pages 174-196, Spring.
    9. Cavit Pakel & Neil Shephard & Kevin Sheppard & Robert F. Engle, 2021. "Fitting Vast Dimensional Time-Varying Covariance Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(3), pages 652-668, July.
    10. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    11. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    12. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    13. Cristiano Varin & Paolo Vidoni, 2005. "A note on composite likelihood inference and model selection," Biometrika, Biometrika Trust, vol. 92(3), pages 519-528, September.
    14. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    15. Tim Bollerslev & Sophia Zhengzi Li & Viktor Todorov, 2014. "Roughing up Beta: Continuous vs. Discontinuous Betas, and the Cross-Section of Expected Stock Returns," CREATES Research Papers 2014-48, Department of Economics and Business Economics, Aarhus University.
    16. Bauer, Gregory H. & Vorkink, Keith, 2011. "Forecasting multivariate realized stock market volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 93-101, January.
    17. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    18. O. E. Barndorff-Nielsen & P. Reinhard Hansen & A. Lunde & N. Shephard, 2009. "Realized kernels in practice: trades and quotes," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 1-32, November.
    19. Diaa Noureldin & Neil Shephard & Kevin Sheppard, 2012. "Multivariate high‐frequency‐based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 907-933, September.
    20. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    21. D. R. Cox, 2004. "A note on pseudolikelihood constructed from marginal densities," Biometrika, Biometrika Trust, vol. 91(3), pages 729-737, September.
    22. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    23. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
    24. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    25. Roxana Chiriac & Valeri Voev, 2011. "Modelling and forecasting multivariate realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(6), pages 922-947, September.
    26. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    27. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    28. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201, November.
    29. Douglas Rivers & Quang Vuong, 2002. "Model selection tests for nonlinear dynamic models," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 1-39, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bollerslev, Tim & Patton, Andrew J. & Quaedvlieg, Rogier, 2018. "Modeling and forecasting (un)reliable realized covariances for more reliable financial decisions," Journal of Econometrics, Elsevier, vol. 207(1), pages 71-91.
    2. Stanislav Anatolyev & Vladimir Pyrlik, 2021. "Shrinkage for Gaussian and t Copulas in Ultra-High Dimensions," CERGE-EI Working Papers wp699, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    3. Christensen, Kim & Christiansen, Charlotte & Posselt, Anders M., 2020. "The economic value of VIX ETPs," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 121-138.
    4. Li, Yifan & Nolte, Ingmar & Vasios, Michalis & Voev, Valeri & Xu, Qi, 2022. "Weighted Least Squares Realized Covariation Estimation," Journal of Banking & Finance, Elsevier, vol. 137(C).
    5. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    6. Qu, Hui & Zhang, Yi, 2022. "Asymmetric multivariate HAR models for realized covariance matrix: A study based on volatility timing strategies," Economic Modelling, Elsevier, vol. 106(C).
    7. Dhaene, Geert & Wu, Jianbin, 2020. "Incorporating overnight and intraday returns into multivariate GARCH volatility models," Journal of Econometrics, Elsevier, vol. 217(2), pages 471-495.
    8. Bauwens, Luc & Otranto, Edoardo, 2020. "Modelling Realized Covariance Matrices: a Class of Hadamard Exponential Models," LIDAM Discussion Papers CORE 2020034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Jin Xisong & Lehnert Thorsten, 2018. "Large portfolio risk management and optimal portfolio allocation with dynamic elliptical copulas," Dependence Modeling, De Gruyter, vol. 6(1), pages 19-46, February.
    10. Giuseppe Buccheri & Davide Pirino & Luca Trapin, 2021. "Managing liquidity with portfolio staleness," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 215-239, June.
    11. Hamori, Shigeyuki & Motegi, Kaiji & Zhang, Zheng, 2019. "Calibration estimation of semiparametric copula models with data missing at random," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 85-109.
    12. BAUWENS Luc, & XU Yongdeng,, 2019. "DCC-HEAVY: A multivariate GARCH model based on realized variances and correlations," LIDAM Discussion Papers CORE 2019025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Rubén Loaiza‐Maya & Michael S. Smith & Worapree Maneesoonthorn, 2018. "Time series copulas for heteroskedastic data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(3), pages 332-354, April.
    14. Kaveh Salehzadeh Nobari, 2021. "Pair copula constructions of point-optimal sign-based tests for predictive linear and nonlinear regressions," Papers 2111.04919, arXiv.org.
    15. Sergii Pypko, 2015. "Volatility Forecast in Crises and Expansions," JRFM, MDPI, vol. 8(3), pages 1-26, August.
    16. Nasri, Bouchra R., 2020. "On non-central squared copulas," Statistics & Probability Letters, Elsevier, vol. 161(C).
    17. Kerem Tuzcuoglu, 2019. "Composite Likelihood Estimation of an Autoregressive Panel Probit Model with Random Effects," Staff Working Papers 19-16, Bank of Canada.
    18. Rewat Khanthaporn, 2022. "Analysis of Nonlinear Comovement of Benchmark Thai Government Bond Yields," PIER Discussion Papers 183, Puey Ungphakorn Institute for Economic Research.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    2. De Lira Salvatierra, Irving & Patton, Andrew J., 2015. "Dynamic copula models and high frequency data," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 120-135.
    3. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Andrea BUCCI, 2017. "Forecasting Realized Volatility A Review," Journal of Advanced Studies in Finance, ASERS Publishing, vol. 8(2), pages 94-138.
    5. Roland Weigand, 2014. "Matrix Box-Cox Models for Multivariate Realized Volatility," Working Papers 144, Bavarian Graduate Program in Economics (BGPE).
    6. BAUWENS, Luc & BRAIONE, Manuela & STORTI, Giuseppe, 2016. "Multiplicative Conditional Correlation Models for Realized Covariance Matrices," LIDAM Discussion Papers CORE 2016041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Fengler, Matthias R. & Okhrin, Ostap, 2016. "Managing risk with a realized copula parameter," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 131-152.
    8. Roxana Halbleib & Valeri Voev, 2011. "Forecasting Covariance Matrices: A Mixed Frequency Approach," CREATES Research Papers 2011-03, Department of Economics and Business Economics, Aarhus University.
    9. Pawel Janus & André Lucas & Anne Opschoor & Dick J.C. van Dijk, 2014. "New HEAVY Models for Fat-Tailed Returns and Realized Covariance Kernels," Tinbergen Institute Discussion Papers 14-073/IV, Tinbergen Institute, revised 19 Aug 2015.
    10. Andrew J. Patton & Kevin Sheppard, 2015. "Good Volatility, Bad Volatility: Signed Jumps and The Persistence of Volatility," The Review of Economics and Statistics, MIT Press, vol. 97(3), pages 683-697, July.
    11. Li, Jia & Patton, Andrew J., 2018. "Asymptotic inference about predictive accuracy using high frequency data," Journal of Econometrics, Elsevier, vol. 203(2), pages 223-240.
    12. Jiayuan Zhou & Feiyu Jiang & Ke Zhu & Wai Keung Li, 2019. "Time series models for realized covariance matrices based on the matrix-F distribution," Papers 1903.12077, arXiv.org, revised Jul 2020.
    13. Francisco Blasques & Andre Lucas & Anne Opschoor & Luca Rossini, 2021. "Tail Heterogeneity for Dynamic Covariance-Matrix-Valued Random Variables: the F-Riesz Distribution," Tinbergen Institute Discussion Papers 21-010/III, Tinbergen Institute.
    14. Roxana Halbleib & Valeri Voev, 2016. "Forecasting Covariance Matrices: A Mixed Approach," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 14(2), pages 383-417.
    15. Bauwens, Luc & Braione, Manuela & Storti, Giuseppe, 2017. "A dynamic component model for forecasting high-dimensional realized covariance matrices," Econometrics and Statistics, Elsevier, vol. 1(C), pages 40-61.
    16. Varneskov, Rasmus & Voev, Valeri, 2013. "The role of realized ex-post covariance measures and dynamic model choice on the quality of covariance forecasts," Journal of Empirical Finance, Elsevier, vol. 20(C), pages 83-95.
    17. Symitsi, Efthymia & Symeonidis, Lazaros & Kourtis, Apostolos & Markellos, Raphael, 2018. "Covariance forecasting in equity markets," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 153-168.
    18. Noureldin, Diaa & Shephard, Neil & Sheppard, Kevin, 2014. "Multivariate rotated ARCH models," Journal of Econometrics, Elsevier, vol. 179(1), pages 16-30.
    19. Fengler, Matthias R. & Gisler, Katja I.M., 2015. "A variance spillover analysis without covariances: What do we miss?," Journal of International Money and Finance, Elsevier, vol. 51(C), pages 174-195.
    20. Anne Opschoor & André Lucas, 2019. "Observation-driven Models for Realized Variances and Overnight Returns," Tinbergen Institute Discussion Papers 19-052/IV, Tinbergen Institute.

    More about this item

    Keywords

    Composite likelihood; forecasting; high frequency data; nonlinear dependence;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fip:fedgfe:2015-50. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/frbgvus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ryan Wolfslayer ; Keisha Fournillier (email available below). General contact details of provider: https://edirc.repec.org/data/frbgvus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.